Skip to main content
Log in

Kolmogorov-Smirnov like test for time-frequency Fourier spectrogram analysis in LISA Pathfinder

Experimental Astronomy Aims and scope Submit manuscript

Abstract

A statistical procedure for the analysis of time-frequency noise maps is presented and applied to LISA Pathfinder mission synthetic data. The procedure is based on the Kolmogorov-Smirnov like test that is applied to the analysis of time-frequency noise maps produced with the spectrogram technique. The influence of the finite size windowing on the statistic of the test is calculated with a Monte Carlo simulation for 4 different windows type. Such calculation demonstrate that the test statistic is modified by the correlations introduced in the spectrum by the finite size of the window and by the correlations between different time bins originated by overlapping between windowed segments. The application of the test procedure to LISA Pathfinder data demonstrates the test capability of detecting non-stationary features in a noise time series that is simulating low frequency non-stationary noise in the system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. w is assumed to be square normalized to 1 so that \(\sum _{i} {w_{i}^{2}} = 1\).

  2. Critical values are cut-off values that define regions where the test statistic has a probability lower than α to be if the null hypothesis is true. α is the significance level such that the confidence level is 1−α. The null hypothesis is rejected if the test statistic lies within this region which is often referred to as the rejection region [10].

  3. The expected model was obtained by a fit procedure of a sample spectra realized with all the noise sources kept stationary at their nominal values.

References

  1. Feller, W.: Ann. Math. Statist. 19(2), 177 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  2. Congedo, G., Ferraioli, L., Hueller, M., De Marchi, F., Vitale, S., Armano, M., Hewitson, M., Nofrarias, M.: Phys. Rev. D 85(12), 122004 (2012)

    Article  ADS  Google Scholar 

  3. Antonucci, F., et al.: Class. Quantum Gravity 28(9), 094002 (2011)

    Article  ADS  Google Scholar 

  4. Antonucci, F., et al.: Class. Quantum Gravity 28(9) (2011)

  5. Antonucci, F., et al.: Class. Quantum Gravity 28(9), 094006 (2011)

    Article  ADS  Google Scholar 

  6. Armano, M., et al.: Class. Quantum Gravity 26(9), 094001 (2009)

    Article  ADS  Google Scholar 

  7. Ferraioli, L., Congedo, G., Hueller, M., Vitale, S., Hewitson, M., Nofrarias, M., Armano, M.: Phys. Rev. D 84, 122003 (2011)

    Article  ADS  Google Scholar 

  8. Percival, D.B., Walden, A.T.: Spectral Analysis for Physical Applications. Cambridge University Press, Cambridge, UK (1993)

    Book  MATH  Google Scholar 

  9. Harris, F.: IEEE Proc. 66(1), 51 (1978)

    Article  ADS  Google Scholar 

  10. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/ (2013)

  11. Ferraioli, L., Hueller, M., Vitale, S.: Class. Quantum Gravity 26(9), 094013 (2009)

    Article  ADS  Google Scholar 

  12. Ferraioli, L., Hueller, M., Vitale, S., Heinzel, G., Hewitson, M., Monsky, A., Nofrarias, M.: Phys. Rev. D 82(4), 042001 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research was supported by the Centre National d’Études Spatiales (CNES).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luigi Ferraioli.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferraioli, L., Armano, M., Audley, H. et al. Kolmogorov-Smirnov like test for time-frequency Fourier spectrogram analysis in LISA Pathfinder. Exp Astron 39, 1–10 (2015). https://doi.org/10.1007/s10686-014-9432-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10686-014-9432-z

Keywords

Navigation